1. Is this a positive or a negative number?
0000 0000 0000 0000 0000 0000 1110 1111 1111 1111 1111 1110 0000 0001 0101 1000 is the binary representation of a positive integer, on 64 bits (8 Bytes).
In a signed binary in one's complement representation, the first bit (the leftmost) indicates the sign, 1 = negative, 0 = positive.
2. Get the binary representation of the positive (unsigned) number.
* Run this step only if the number is negative *
Flip all the bits of the signed binary in one's complement representation (reverse the digits) - replace the bits set on 1 with 0s and the bits on 0 with 1s:
* Not the case - the number is positive *
3. Map the unsigned binary number's digits versus the corresponding powers of 2 that their place value represent:
263
0 262
0 261
0 260
0 259
0 258
0 257
0 256
0 255
0 254
0 253
0 252
0 251
0 250
0 249
0 248
0 247
0 246
0 245
0 244
0 243
0 242
0 241
0 240
0 239
1 238
1 237
1 236
0 235
1 234
1 233
1 232
1 231
1 230
1 229
1 228
1 227
1 226
1 225
1 224
1 223
1 222
1 221
1 220
1 219
1 218
1 217
1 216
0 215
0 214
0 213
0 212
0 211
0 210
0 29
0 28
1 27
0 26
1 25
0 24
1 23
1 22
0 21
0 20
0
4. Multiply each bit by its corresponding power of 2 and add all the terms up.
0000 0000 0000 0000 0000 0000 1110 1111 1111 1111 1111 1110 0000 0001 0101 1000(2) =
(0 × 263 + 0 × 262 + 0 × 261 + 0 × 260 + 0 × 259 + 0 × 258 + 0 × 257 + 0 × 256 + 0 × 255 + 0 × 254 + 0 × 253 + 0 × 252 + 0 × 251 + 0 × 250 + 0 × 249 + 0 × 248 + 0 × 247 + 0 × 246 + 0 × 245 + 0 × 244 + 0 × 243 + 0 × 242 + 0 × 241 + 0 × 240 + 1 × 239 + 1 × 238 + 1 × 237 + 0 × 236 + 1 × 235 + 1 × 234 + 1 × 233 + 1 × 232 + 1 × 231 + 1 × 230 + 1 × 229 + 1 × 228 + 1 × 227 + 1 × 226 + 1 × 225 + 1 × 224 + 1 × 223 + 1 × 222 + 1 × 221 + 1 × 220 + 1 × 219 + 1 × 218 + 1 × 217 + 0 × 216 + 0 × 215 + 0 × 214 + 0 × 213 + 0 × 212 + 0 × 211 + 0 × 210 + 0 × 29 + 1 × 28 + 0 × 27 + 1 × 26 + 0 × 25 + 1 × 24 + 1 × 23 + 0 × 22 + 0 × 21 + 0 × 20)(10) =
(0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 549 755 813 888 + 274 877 906 944 + 137 438 953 472 + 0 + 34 359 738 368 + 17 179 869 184 + 8 589 934 592 + 4 294 967 296 + 2 147 483 648 + 1 073 741 824 + 536 870 912 + 268 435 456 + 134 217 728 + 67 108 864 + 33 554 432 + 16 777 216 + 8 388 608 + 4 194 304 + 2 097 152 + 1 048 576 + 524 288 + 262 144 + 131 072 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 256 + 0 + 64 + 0 + 16 + 8 + 0 + 0 + 0)(10) =
(549 755 813 888 + 274 877 906 944 + 137 438 953 472 + 34 359 738 368 + 17 179 869 184 + 8 589 934 592 + 4 294 967 296 + 2 147 483 648 + 1 073 741 824 + 536 870 912 + 268 435 456 + 134 217 728 + 67 108 864 + 33 554 432 + 16 777 216 + 8 388 608 + 4 194 304 + 2 097 152 + 1 048 576 + 524 288 + 262 144 + 131 072 + 256 + 64 + 16 + 8)(10) =
1 030 792 020 312(10)
5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
0000 0000 0000 0000 0000 0000 1110 1111 1111 1111 1111 1110 0000 0001 0101 1000(2) = 1 030 792 020 312(10)
The signed binary number in one's complement representation 0000 0000 0000 0000 0000 0000 1110 1111 1111 1111 1111 1110 0000 0001 0101 1000(2) converted and written as an integer in decimal system (base ten):
0000 0000 0000 0000 0000 0000 1110 1111 1111 1111 1111 1110 0000 0001 0101 1000(2) = 1 030 792 020 312(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.